Thanks, Brent and Bruno. You are kind to respond. The point I wanted to approach (far approach, indeed) is that whatever we derive (mentally) about Nature comes from our human mind, be it binary or not. And: it is not BINDING (restricting?) upon Nature, there may be more we cannot even imagine within our limited capabilities. We think in our 'model of knowables' and it is incredible how far we got. A figment of a physical world, an 'almost' perfect technology with a reductionist (conventional) science and I don't even mention: math.
I read your discussions with awe and keep my agnostic indeterminism. JohnM On Sat, May 26, 2012 at 6:06 PM, meekerdb <meeke...@verizon.net> wrote: > On 5/26/2012 9:35 AM, John Mikes wrote: > > Brent wrote: > > *1. Presumably those true things would not be 'real'. Only provable > things would be true of reality.* > > > Just to be clear, I didn't write 1. above. But I did write 2. below. > > > ** > *2. Does arithmetic have 'finite information content'? Is the axiom of > succession just one or is it a schema of infinitely many axioms?* > ** > Appreciable, even in layman's logic. > > In '#1' - I question "provable" since in my agnosticism an 'evidence' is > partial only, leaving open lots of (so far?) unknown/able aspects to be > covered. In the infinity(?) of the "world" also the contrary of an evidence > may be 'true'. > > > As Bruno said, "Provable is always relative to some axioms and rules of > inference. It is quite independent of "true of reality". Which is why > I'm highly suspicious of ideas like deriving all of reality from > arithmetic, which we know only from axioms and inferences. > > > > #2 is a technically precise formulation of what I tried to express in my > post to Bruno. > IFF!!! "anything" (i.e. everything) can be expressed by numerals, the > information included into arithmetic * IS* infinite, > > > I see no reason to suppose that. Everything ever expressed so far has > been done with a finite part of arithmetic. Assuming every integer has a > successor is just a convenience for modeling things; you don't have to > worry about running out of counters. There is a book "Ad Infinitum, The > Ghost in Turing's Machine" by Rotman that proposes what he calls > "non-euclidean arithmetic" which does not assume the integers are > infinite. I can't really recommend the book because most of it is written > in the style of French deconstructionist philosophy, but the Appendix has > some interesting ideas. > > > however as it seems: in our (restricted) view of "the world" (Nature?) > there seem to be NO numbers to begin with. > In our human 'translation' we see 1,2, or 145, or a million "OF SOMETHING" > - no the (integer?) numerals. > > Axioms? in my vocabulary: imagined things, necessary for certain theories > we cannot substantiate otherwise. > > > Axioms are just part of a logical, i.e. self-consistent, system. > Mathematicians don't even care if they are "true of reality". They may or > may not refer to imagined things; they are just assumed true for some > inferences. I could take "I am typing on a keyboard" as an axiom, which I > also happen to think is true, or I could take "I am a projection in a > Hilbert space" which might be true, but is much more dubious. > > > In another logic than human, in another figment of a "physical world" > different axioms would serve science. > > > Logic is about the relations of propositions, statements in language. > Humans already have invented different logics. > > > 2+2=4? not necessarily in the (fictitious) "octimality" of the > '[Zarathustran' aliens in the Cohen-Stewart books > (still product of human minds). > > > 2+2=11 > > Brent > "The world consists of 10 kinds of people. Those who think in binary and > those who don't. > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To post to this group, send email to everything-list@googlegroups.com. > To unsubscribe from this group, send email to > everything-list+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
